Nationwide, the UK's largest building society, has benefited from being seen as a haven from the credit crunch.
Nationwide is owned by its members instead of shareholders
It said that savings deposits in the six months to the end of September had nearly doubled to £4.1bn.
That was partly as a result of the purchase of its smaller rival Portman, which was completed in September.
But Nationwide's chief executive Graham Beale said: "There's no doubt we've seen a flight to quality as savers seek a safe haven at a very difficult time."
The credit crunch was set off by record defaults in the US sub-prime mortgage market leaving many banks worldwide holding debt of questionable value.
That led to the effective closing down of the wholesale money markets, in which banks lend money to each other, because they were uncertain about how much surplus cash they have to lend and are not sure which other banks are creditworthy.
In the UK, Northern Rock borrowed the highest proportion of the money it lent from the wholesale markets and so was particularly hard hit.
Nationwide said today that it was currently getting 29% of financing from wholesale markets, which is lower than most of its rivals.
About £1.8bn of savings flowed in during September, which suggests that some of the people who queued up to withdraw their money from Northern Rock then deposited it at Nationwide.
The building society reported its six-month underlying profit was £394m, up 29% compared with the same period of 2006.
Its share of net mortgage lending fell to about 5.7% in the period, down from its typical market share of more than 10%.
Nationwide said this reflected its "cautious approach to lending in a fiercely competitive market" and predicted that its share of new mortgages would be about 6% for the next six months as well.
The building society said it had continued to see large inflows of savings in October and November, and this had enabled it to fund all of its residential mortgage lending for the period through deposits.